Exponential growth question for the mathematicians who love family trees

Here's something for the mathematicians that are also genealogists, since those subjects get intertwined a lot. I put this under Number Theory because of the exponential growth that comes with family trees. Anyway, I'm working on my mum's ancestry - one of her 16 great-great-grandparents was born to Irish immigrants, but the other 15 were English - and I've heard 'every English person descends from Edward III'. Counting back in a "two
generations per every 50 years" pattern from the 1970s, there are 524,288 direct ancestors for my mum by the nineteenth generation back circa the 1490s. I'm guessing about 492,000 of that lot were English at a time when England's population was 2.14 million.

I therefore thought it was mathematically sensible to assume that we have a roughly 1 in 4 chance of being descended from one of the Tudors because of this. It just makes sense that Henry VII and Elizabeth of York might well make an appearance in that complex web somewhere, even if I haven't proven it yet. Every European descends from Charlemagne because of the sheer power of exponential growth in ancestry. I'm thinking the trail starts way back with Lady Jane Grey's sister Catherine or their maternal cousin Lady Margaret Clifford, since they both married into families that left English descendants. I realise this is a VERY niche question, but I'm sure I can't be the only one who likes royalty, family trees and maths. I guess what I'm asking is "although I haven't proved the link, could I be on to something with my calculations and logic?"